The difference in specific gravity of Al vs Ti is 2.7 versus 4.506. So when density in factored in, a aluminum pot has to be 17.96 times thicker than a titanium pot.
But these figures are theoretical. There are many other factors in real life which would play an important role in stove performance.
Specific gravity has absolutely nothing to do with calculating heat transfer.
Pots are not just flat plates; they're essentially pipes that are capped at the bottom. To compare the efficiency of heating a set volume of water, you've got to take into consideration the heat transfer into the water a) through the base, b) from the base through vertical walls of the pot both, as well as the c) heat lost to the air through the walls and lid of the pot.
© is critical. Pot material or wall thickness is probably negligible as compared to flame geometry and pot geometry, both for boiling water quickly and efficiently (two completely different criteria).
To say Layton's real world tests are worthless reveals a lack of understanding of the overall problem. A couple of degrees difference in air temperature is negligible, considering that the conductivity of water is 240 times that of air, and that of any metal is thousands of times greater. Heat lost to the air due to big flame/small diameter pot is not going to be substantially effected by such minor changes either.
Air is 240 times less conductive than water, so any heat pumped into the metal is going into the water, not the air.
Any heat not transfered directly through the bottom of the pot and into the water is either a) lost to the air b) conducted from the air into the water through the walls of the pot or c) conducted directly through the walls of the pot into the water. Since air is 240 times less conductive than water, most of the heat transfered to the walls of the pot will go into the water. What actually happens depends on flame versus pot geometry. If the flame envelopes the walls of the pot, a thinner pots is probably better. If not, a thicker walled pot, which transfers more heat into pot's walls and into the water (rather than surrounding air),might actually heat water more efficiently. A thicker pot will
BTW,